Acceleration Due to Gravity and Its Variation
Effect of altitude, depth and rotation of the earth. (Physics › Gravitation, NEET UG syllabus.)
What is Acceleration Due to Gravity and Its Variation?
The acceleration experienced by an object solely due to the gravitational force of a celestial body, typically Earth.
Key formula / rule: Acceleration due to gravity on Earth's surface
Key points
- Define acceleration due to gravity and state its standard value.
- Derive and apply the formula for variation of 'g' with altitude (both exact and approximate).
- Derive and apply the formula for variation of 'g' with depth.
- Explain how Earth's rotation affects 'g' and apply the relevant formula for latitude variation.
Common exam trap
Confusing the exact formula for altitude with the approximation, or vice-versa.
Definitions
- Term
Acceleration due to gravity (g)
- Meaning
The acceleration experienced by an object solely due to the gravitational force of a celestial body, typically Earth.
- Term
Equatorial plane
- Meaning
An imaginary plane passing through the center of the Earth and perpendicular to its axis of rotation, where latitude is 0°.
- Term
Polar regions
- Meaning
The areas around the Earth's geographic poles, where latitude is 90°.
Learning objectives
Define acceleration due to gravity and state its standard value.
Derive and apply the formula for variation of 'g' with altitude (both exact and approximate).
Derive and apply the formula for variation of 'g' with depth.
Explain how Earth's rotation affects 'g' and apply the relevant formula for latitude variation.
Compare and contrast the effects of altitude, depth, and rotation on 'g'.
Solve numerical problems involving variations in 'g' under different conditions.
Formulae
- Name
Acceleration due to gravity on Earth's surface
- Note
M is Earth's mass, R is Earth's radius, G is Universal Gravitational Constant.
- Expression
g = GM/R²
- Name
Acceleration due to gravity at altitude h (exact)
- Note
Valid for any height h above the Earth's surface.
- Expression
gh = GM/(R+h)²
- Name
Acceleration due to gravity at altitude h (approximation)
- Note
Valid for heights h much smaller than Earth's radius (h << R).
- Expression
gh ≈ g(1 - 2h/R)
- Name
Acceleration due to gravity at depth d
- Note
Valid for depth d below the Earth's surface. gd = 0 at d=R (Earth's center).
- Expression
gd = g(1 - d/R)
- Name
Acceleration due to gravity at latitude λ (due to rotation)
- Note
ω is Earth's angular speed, λ is the latitude. 'g' here is the value without considering rotation.
- Expression
g_λ = g - Rω²cos²λ
Prerequisites
Newton's Law of Universal Gravitation (F = GMm/r²)
Concept of gravitational field strength
Basic understanding of circular motion and centrifugal force
Knowledge of Earth's properties (radius, mass, angular velocity)
Basic algebra and approximations (binomial expansion)
Common mistakes
Confusing the exact formula for altitude with the approximation, or vice-versa.
Incorrectly applying the sign in the latitude variation formula (it's a reduction, so subtract Rω²cos²λ).
Assuming 'g' is constant everywhere on Earth's surface.
Forgetting that 'g' becomes zero at the Earth's center, not just very small.
Not understanding that only the mass of the sphere below the object contributes to gravity when calculating 'g' at depth.
Keywords
Acceleration due to gravity
gravitation
altitude
depth
latitude
Earth's rotation
centrifugal force
gravitational constant
Earth's radius
angular velocity
Practice preview
If 'g' is the acceleration due to gravity on the Earth's surface, the acceleration due to gravity at a depth 'd' below the Earth's surface is given by:…
easy
At what height 'h' above the Earth's surface will the acceleration due to gravity be the same as that at a depth 'd' below the Earth's surface, assuming h and d are small compared to Earth's radius R?…
medium
Which of the following statements about the acceleration due to gravity (g) is INCORRECT?…
medium